Simplify the following expression: $q = \dfrac{8t^2 - 80t}{-80t}$ You can assume $t \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $8t^2 - 80t = (2\cdot2\cdot2 \cdot t \cdot t) - (2\cdot2\cdot2\cdot2\cdot5 \cdot t)$ The denominator can be factored: $-80t = - (2\cdot2\cdot2\cdot2\cdot5 \cdot t)$ The greatest common factor of all the terms is $8t$ Factoring out $8t$ gives us: $q = \dfrac{(8t)(t - 10)}{(8t)(-10)}$ Dividing both the numerator and denominator by $8t$ gives: $q = \dfrac{t - 10}{-10}$